a class for evaluating a Butterworth filter transfer function. More...

#include <SimButterworthBandpass.h>

Inheritance diagram for casacore::SimButterworthBandpass< T >:

Public Types
enum	{ CENTER, MINCUTOFF, MAXCUTOFF, PEAK }
	Enumeration of the function parameters. More...

Public Types inherited from casacore::Function1D< T >
typedef const T *	FunctionArg

Public Types inherited from casacore::Function< T, U >
typedef FunctionTraits< T > ::ArgType	ArgType

typedef const ArgType *	FunctionArg

Public Member Functions
	SimButterworthBandpass ()
	create a zero-th order (all-pass) Butterworth bandpass function. More...

	SimButterworthBandpass (const uInt minord, const uInt maxord, const T &mincut=T(-1), const T &maxcut=T(1), const T &center=T(0), const T &peak=T(1))
	create a Butterworth bandpass function. More...

	SimButterworthBandpass (const RecordInterface &gr, T mincut=T(-1), T maxcut=T(1), T center=T(0), T peak=T(1))
	create a fully specified Butterworth bandpass in which the low and high pass orders are stored in a Record More...

	SimButterworthBandpass (const SimButterworthBandpass &other)
	create a copy of another Butterworth bandpass function More...

SimButterworthBandpass< T > &	operator= (const SimButterworthBandpass< T > &other)
	copy(deep) another Butterworth function More...

virtual	~SimButterworthBandpass ()
	Destructor. More...

virtual T	eval (const typename FunctionTraits< T >::ArgType *x) const
	Evaluate the bandpass at "x". More...

void	setCenter (const T &x)
	set the center of the bandpass. More...

const T &	getCenter () const
	return the center of the bandpass. More...

void	setMinCutoff (const T &x)
	set the characteristic minimum (high-pass) cutoff value. More...

void	setMaxCutoff (const T &x)
	set the characteristic maximum (low-pass) cutoff value. More...

void	setMinOrder (uInt order)
	set the order of the Butterworth function for the minimum (high-pass) portion of the bandpass More...

void	setMaxOrder (uInt order)
	set the order of the Butterworth function for the maximum (low-pass) portion of the bandpass More...

const T &	getMinCutoff () const
	return the characteristic minimum (high-pass) cutoff value. More...

const T &	getMaxCutoff () const
	return the characteristic maximum (low-pass) cutoff value. More...

uInt	getMinOrder () const
	return the order of the Butterworth function for the minimum (high-pass) portion of the bandpass More...

uInt	getMaxOrder () const
	return the order of the Butterworth function for the maximum (low-pass) portion of the bandpass More...

void	setPeak (T val)
	set the scale of the function by setting its peak value. More...

const T &	getPeak () const
	return the scale of the function More...

virtual void	setMode (const RecordInterface &mode)
	get/set the function mode. More...

virtual void	getMode (RecordInterface &mode) const

virtual Bool	hasMode () const
	return True if the implementing function supports a mode. More...

virtual Function< T > *	clone () const
	clone this function More...

Public Member Functions inherited from casacore::Function1D< T >
	Function1D ()
	Constructors. More...

	Function1D (const uInt n)

	Function1D (const Vector< T > &in)

	Function1D (const FunctionParam< T > &other)

	Function1D (const Function1D< T, T > &other)

	Function1D (const Function1D< W, X > &other)

virtual	~Function1D ()
	Destructor. More...

virtual uInt	ndim () const
	Returns the number of dimensions of function. More...

Public Member Functions inherited from casacore::Function< T, U >
	Function ()
	Constructors. More...

	Function (const uInt n)

	Function (const Vector< T > &in)

	Function (const FunctionParam< T > &other)

template<class W , class X >
	Function (const Function< W, X > &other)

	Function (const Function< T, U > &other)

virtual	~Function ()
	Destructor. More...

uInt	nparameters () const
	Returns the number of parameters. More...

virtual U	eval (FunctionArg x) const =0
	Evaluate the function object. More...

T &	operator[] (const uInt n)
	Manipulate the nth parameter (0-based) with no index check. More...

const T &	operator[] (const uInt n) const

virtual U	operator() () const
	Evaluate this function object at `x`or at `x, y`. More...

virtual U	operator() (const ArgType &x) const

virtual U	operator() (const Vector< ArgType > &x) const

virtual U	operator() (FunctionArg x) const

virtual U	operator() (const ArgType &x, const ArgType &y) const

virtual U	operator() (const ArgType &x, const ArgType &y, const ArgType &z) const

virtual const String &	name () const
	Specify the name associated with the function (default will be `unknown`) More...

Bool &	mask (const uInt n)
	Manipulate the mask associated with the nth parameter (e.g. More...

const Bool &	mask (const uInt n) const

const FunctionParam< T > &	parameters () const
	Return the parameter interface. More...

FunctionParam< T > &	parameters ()

const Vector< ArgType > &	argp () const
	Get `arg_p` and `parset_p`. More...

Bool	parsetp () const

void	lockParam ()
	Compiler cannot always find the correct 'const' version of parameter access. More...

void	unlockParam ()

ostream &	print (ostream &os) const
	Print the function (i.e. More...

virtual Function< typename FunctionTraits< T >::DiffType > *	cloneAD () const

virtual Function< typename FunctionTraits< T >::BaseType > *	cloneNonAD () const

Public Member Functions inherited from casacore::Functional< FunctionTraits< T >::ArgType, U >
virtual	~Functional ()
	Destructor. More...

virtual U	operator() (const FunctionTraits< T >::ArgType &x) const =0
	Map a Domain `x` into a Range `y` value. More...

Public Member Functions inherited from casacore::Functional< Vector< FunctionTraits< T >::ArgType >, U >
virtual	~Functional ()
	Destructor. More...

virtual U	operator() (const Vector< FunctionTraits< T >::ArgType > &x) const =0
	Map a Domain `x` into a Range `y` value. More...

Private Attributes
uInt	nl_p
	Minimum order. More...

uInt	nh_p
	Maximum order. More...

Additional Inherited Members
Protected Attributes inherited from casacore::Function< T, U >
FunctionParam< T >	param_p
	The parameters and masks. More...

Vector< ArgType >	arg_p
	Aid for non-contiguous argument storage. More...

Bool	parset_p
	Indicate parameter written. More...

Bool	locked_p
	Indicate that parameters are expected to be locked from changing. More...

Detailed Description

template<class T>
class casacore::SimButterworthBandpass< T >

a class for evaluating a Butterworth filter transfer function.

Intended use:

Public interface

Review Status

Reviewed By:: wbrouw
Date Reviewed:: 2001/11/14
Test programs:: tSimButterworthBandpass

Prerequisite

FunctionParam class
Function1D

Etymology

"Butterworth" refers to the Butterworth function for describing filter transfer functions (Butterworth, S, "On the theory of filter amplifiers," Wireless Engineer, vol. 7 pp. 536-541, October 1930). "Bandpass" reflects that the transfer function is has both low and high frequency cutoffs. "Sim" indicates that this implementation is not necessarily appropriate characterizing real bandpass filters; in the future, there may be a more general class called simply "Butterworth".

Synopsis

This function class simulates the (amplitude) transfer function for a wideband bandpass filter constructed from the combination of a low-pass and a high-pass Butterworth filter.

In analog electronic filter design, a Butterworth low-pass filter is one in which the amplitude transfer function, |H(jw)| (where j = sqrt(-1) and w is the angular frequency), is given by:

|H(jw)| = 1 / sqrt(1 + (w/w_c)^(2*n))

where n refers to the filter "order" and w_c is the "cutoff frequency". When w = w_c, the filter output is 1/sqrt(2) that of the input, and the higher the order, the steeper the drop off towards zero and the closer the approximation to a idealized step function.

Filter theory provides transformations for deriving transfer functions of high-pass and band-pass filters which reflect how the electrical circuits actually work. However, to simplify this class's implementation and to make the transfer function behavior more predictable by the naive user, THIS CLASS DOES NOT ACTUALLY USE THE PROPER TRANSFORMATIONS (see Etymology section above). Instead, the Butterworth bandpass transfer function is approximated by low pass component, given above, combined with a pseudo high-pass function that is of the same form but with w substituted with -w. Both components are shifted such that its peak transfer point is at a given "center" position. The cutoff value and order can be set independently for both ends of the passband.

Example

// Create a bandpass function centered on x=0.8 and cutoffs at 0 and 2.5.
// The orders of the drop-offs will 4 at the low end and 5 at the high
// end.  The peak will by 1.0 by default.
SimButterworthBandpass<Double> butt(4, 5, 0, 2.5, 0.8);
Double z = butt(1);    // z = 1.0
z = butt(0);           // z = 1/sqrt(2)
z = butt(2.5);         // z = 1/sqrt(2)
z = butt(-25);         // z ~ 9.24e-9 ~ 0
// change the low-end cutoff to -25.0
butt.setMinCutoff(-25);
z = butt(-25);         // z = 1/sqrt(2)

Motivation

This class was created to simulate systemtic Butterworth bandpasses within the simulator tool. It can used by the SimBJones class to vary the bandpass in a predictable way. However, it has limited value for real filter analysis, and it is not expected to be a realistic representation of real bandpass filters in use with radio telescopes backends.

Template Type Argument Requirements (T)

T should have standard numerical operators. Current implementation only tested for real types (and their AutoDiffs).

Thrown Exceptions

Assertion if indices out-of-range

To Do

Nothing I know of

Definition at line 137 of file SimButterworthBandpass.h.

Member Enumeration Documentation

template<class T>

anonymous enum

Enumeration of the function parameters.

Enumerator
CENTER
MINCUTOFF
MAXCUTOFF
PEAK

Definition at line 142 of file SimButterworthBandpass.h.

Constructor & Destructor Documentation

template<class T>

casacore::SimButterworthBandpass< T >::SimButterworthBandpass ( )

create a zero-th order (all-pass) Butterworth bandpass function.

template<class T>

casacore::SimButterworthBandpass< T >::SimButterworthBandpass	(	const uInt	minord,
		const uInt	maxord,
		const T &	mincut = `T(-1)`,
		const T &	maxcut = `T(1)`,
		const T &	center = `T(0)`,
		const T &	peak = `T(1)`
	)

create a Butterworth bandpass function.

template<class T>

casacore::SimButterworthBandpass< T >::SimButterworthBandpass	(	const RecordInterface &	gr,
		T	mincut = `T(-1)`,
		T	maxcut = `T(1)`,
		T	center = `T(0)`,
		T	peak = `T(1)`
	)

explicit

create a fully specified Butterworth bandpass in which the low and high pass orders are stored in a Record

template<class T>

casacore::SimButterworthBandpass< T >::SimButterworthBandpass ( const SimButterworthBandpass< T > & other )

create a copy of another Butterworth bandpass function

template<class T>

virtual casacore::SimButterworthBandpass< T >::~SimButterworthBandpass ( )

virtual

Destructor.

Member Function Documentation

template<class T>

virtual Function<T>* casacore::SimButterworthBandpass< T >::clone ( ) const

inlinevirtual

clone this function

Implements casacore::Function< T, U >.

Reimplemented in casacore::MarshButterworthBandpass< T >.

Definition at line 248 of file SimButterworthBandpass.h.

template<class T>

virtual T casacore::SimButterworthBandpass< T >::eval ( const typename FunctionTraits< T >::ArgType * x ) const

virtual

Evaluate the bandpass at "x".

template<class T>

const T& casacore::SimButterworthBandpass< T >::getCenter ( ) const

inline

return the center of the bandpass.

This is the x-ordinate value that evaluates to the peak of the function.

Definition at line 181 of file SimButterworthBandpass.h.

References casacore::SimButterworthBandpass< T >::CENTER, and casacore::Function< T, U >::param_p.

template<class T>

const T& casacore::SimButterworthBandpass< T >::getMaxCutoff ( ) const

inline

return the characteristic maximum (low-pass) cutoff value.

At this x-ordinate value, the function has a value reduced 30 dB from its peak.

Definition at line 209 of file SimButterworthBandpass.h.

References casacore::SimButterworthBandpass< T >::MAXCUTOFF, and casacore::Function< T, U >::param_p.

template<class T>

uInt casacore::SimButterworthBandpass< T >::getMaxOrder ( ) const

inline

return the order of the Butterworth function for the maximum (low-pass) portion of the bandpass

Definition at line 217 of file SimButterworthBandpass.h.

References casacore::SimButterworthBandpass< T >::nh_p.

template<class T>

const T& casacore::SimButterworthBandpass< T >::getMinCutoff ( ) const

inline

return the characteristic minimum (high-pass) cutoff value.

At this x-ordinate value, the function has a value reduced 30 dB from its peak.

Definition at line 204 of file SimButterworthBandpass.h.

References casacore::SimButterworthBandpass< T >::MINCUTOFF, and casacore::Function< T, U >::param_p.

template<class T>

uInt casacore::SimButterworthBandpass< T >::getMinOrder ( ) const

inline

return the order of the Butterworth function for the minimum (high-pass) portion of the bandpass

Definition at line 213 of file SimButterworthBandpass.h.

References casacore::SimButterworthBandpass< T >::nl_p.

template<class T>

virtual void casacore::SimButterworthBandpass< T >::getMode ( RecordInterface & mode ) const

virtual

Reimplemented from casacore::Function< T, U >.

template<class T>

const T& casacore::SimButterworthBandpass< T >::getPeak ( ) const

inline

return the scale of the function

Definition at line 224 of file SimButterworthBandpass.h.

References casacore::Function< T, U >::param_p, and casacore::SimButterworthBandpass< T >::PEAK.

template<class T>

virtual Bool casacore::SimButterworthBandpass< T >::hasMode ( ) const

virtual

return True if the implementing function supports a mode.

This implementation always returns True.

Reimplemented from casacore::Function< T, U >.

template<class T>

SimButterworthBandpass<T>& casacore::SimButterworthBandpass< T >::operator= ( const SimButterworthBandpass< T > & other )

copy(deep) another Butterworth function

Referenced by casacore::MarshButterworthBandpass< T >::operator=().

template<class T>

void casacore::SimButterworthBandpass< T >::setCenter ( const T & x )

inline

set the center of the bandpass.

This is the x-ordinate value that evaluates to the peak of the function.

Definition at line 177 of file SimButterworthBandpass.h.

References casacore::SimButterworthBandpass< T >::CENTER, and casacore::Function< T, U >::param_p.

template<class T>

void casacore::SimButterworthBandpass< T >::setMaxCutoff ( const T & x )

inline

set the characteristic maximum (low-pass) cutoff value.

At this x-ordinate value, the function has a value reduced 30 dB from its peak.

Definition at line 191 of file SimButterworthBandpass.h.

References casacore::SimButterworthBandpass< T >::MAXCUTOFF, and casacore::Function< T, U >::param_p.

template<class T>

void casacore::SimButterworthBandpass< T >::setMaxOrder ( uInt order )

inline

set the order of the Butterworth function for the maximum (low-pass) portion of the bandpass

Definition at line 199 of file SimButterworthBandpass.h.

References casacore::SimButterworthBandpass< T >::nh_p.

template<class T>

void casacore::SimButterworthBandpass< T >::setMinCutoff ( const T & x )

inline

set the characteristic minimum (high-pass) cutoff value.

At this x-ordinate value, the function has a value reduced 30 dB from its peak.

Definition at line 186 of file SimButterworthBandpass.h.

References casacore::SimButterworthBandpass< T >::MINCUTOFF, and casacore::Function< T, U >::param_p.

template<class T>

void casacore::SimButterworthBandpass< T >::setMinOrder ( uInt order )

inline

set the order of the Butterworth function for the minimum (high-pass) portion of the bandpass

Definition at line 195 of file SimButterworthBandpass.h.

References casacore::SimButterworthBandpass< T >::nl_p.

template<class T>

virtual void casacore::SimButterworthBandpass< T >::setMode ( const RecordInterface & mode )

virtual

get/set the function mode.

This is an alternate way to get/set the non-coefficient data for this function. The supported record fields are as follows:

Field Name     Type            Role

minOrder   TpInt   the order of the Butterworth function for the 
minimum (high-pass) portion of the bandpass
maxOrder   TpInt   the order of the Butterworth function for the 
maximum (low-pass) portion of the bandpass
An exception is thrown if either value is less than zero

Reimplemented from casacore::Function< T, U >.

template<class T>

void casacore::SimButterworthBandpass< T >::setPeak ( T val )

inline

set the scale of the function by setting its peak value.

By default, the peak value is T(1);

Definition at line 221 of file SimButterworthBandpass.h.

References casacore::Function< T, U >::param_p, and casacore::SimButterworthBandpass< T >::PEAK.